Conversion from decimal to hexadecimal

Feb 2013
50
0
Charlotte, NC
How do I convert 2,000 from decimal to hexadecimal?
 

Prove It

MHF Helper
Aug 2008
12,897
5,001
How do I convert 2,000 from decimal to hexadecimal?
It helps if you think of the columns in your hexadecimal number as powers of 16, so your first digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}\), the second digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}\), the third digit will represent how many lots of \(\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}\), etc. Notice that \(\displaystyle \displaystyle \begin{align*} 16^2 = 256 \end{align*}\) and \(\displaystyle \displaystyle \begin{align*} 16^3 = 4069 \end{align*}\), so that means in hexadecimal your number can only have three digits.

Now notice that \(\displaystyle \displaystyle \begin{align*} \frac{2000}{16^2} = 7\,\frac{208}{16^2} \end{align*}\), so your \(\displaystyle \displaystyle \begin{align*} 16^2 \end{align*}\) digit is \(\displaystyle \displaystyle \begin{align*} 7 \end{align*}\). You are left with \(\displaystyle \displaystyle \begin{align*} 208 \end{align*}\).

Now notice that \(\displaystyle \displaystyle \begin{align*} \frac{208}{16} = 13 \end{align*}\), so your \(\displaystyle \displaystyle \begin{align*} 16^1 \end{align*}\) digit will have to be a \(\displaystyle \displaystyle \begin{align*} d \end{align*}\) (which is the 13th digit).

Since there is no remainder, your \(\displaystyle \displaystyle \begin{align*} 16^0 \end{align*}\) term has to be \(\displaystyle \displaystyle \begin{align*} 0 \end{align*}\).


Therefore \(\displaystyle \displaystyle \begin{align*} 2000_{10} = 7d0_{16} \end{align*}\).
 
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May 2013
12
0
London
below he shoe all the conversion of decimal to hexadecimal. i am also confusing about this problem thanks for solving......
 
Jun 2013
4
0
New York
16^3 = 4096, which is too big

16^2 = 256, which is smaller than 2000, so divide 2000 by 256
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
16 divides into 2600 121 times with remainder 0. That means that 2600= 121(16)+ 0.
16 divides into 121 7 times with remainder 9. That means that 121= 7(16)+ 9.

Putting those together 2600= (7(16)+ 9)(16)+ 0= 7(16)^2+ 9(16)+ 0 so 2600 base 10 is 790 base 16.
 
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Prove It

MHF Helper
Aug 2008
12,897
5,001
16 divides into 2600 121 times with remainder 0. That means that 2600= 121(16)+ 0.
16 divides into 121 7 times with remainder 9. That means that 121= 7(16)+ 9.

Putting those together 2600= (7(16)+ 9)(16)+ 0= 7(16)^2+ 9(16)+ 0 so 2600 base 10 is 790 base 16.
I'm not sure why you posted this, the number the OP was trying to convert was 2000, not 2600...

Also, your answer can not possibly be right, as 2000 in hexadecimal is 7d0, and 2600 is greater than this, yet you have gotten 790 in hexadecimal which is smaller...
 
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Soroban

MHF Hall of Honor
May 2006
12,028
6,341
Lexington, MA (USA)
Hello, Civy71!

How do I convert 2,000 from decimal to hexadecimal?

There is an algorithm which no one has mentioned.

[1] Divide the number by the base. .Note the quotient and remainder.

[2] Divide the quotient by the base. .Note the quotient and remainder.

[3] Repeat step [2] until the zero quotient is attained.

[4] Read up the remainders.


. . \(\displaystyle \begin{array}{cccccc} 2000 \div 16 &=& 125 & \text{rem. }0 \\ 125 \div 16 &=& 7 & \text{rem. }13 \\ 7 \div 16 &=& 0 & \text{rem. }7 \end{array}\begin{array}{c}\uparrow \\ \uparrow \end{array}\)

Therefore: .\(\displaystyle 2000_{10} \;=\;7D0_{16}\)
 
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